Automated reservoir modeling using deep generative networks

ABSTRACT

A method for generating one or more reservoir models using machine learning is provided. Generating reservoir models is typically a time-intensive idiosyncratic process. However, machine learning may be used to generate one or more reservoir models that characterize the subsurface. The machine learning may use geological data, geological concepts, reservoir stratigraphic configurations, and one or more input geological models in order to generate the one or more reservoir models. As one example, a generative adversarial network (GAN) may be used as the machine learning methodology. The GAN includes two neural networks, including a generative network (which generates candidate reservoir models) and a discriminative network (which evaluates the candidate reservoir models), contest with each other in order to generate the reservoir models.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application62/878,981, filed Jul. 26, 2019, entitled “Automated Reservoir ModelingUsing Deep Generative Networks”; of U.S. Provisional Application62/826,095, filed Mar. 29, 2019, entitled “Data Augmentation for SeismicInterpretation Systems and Methods,” and of U.S. Provisional Application62/777,941, filed Dec. 11, 2018, entitled “Automated SeismicInterpretation-Guided Inversion”; and the entirety of which areincorporated by reference herein.

TECHNICAL FIELD

This disclosure relates generally to the field of geophysicalprospecting and, more particularly, to seismic prospecting forhydrocarbon management and related data processing. Specifically,exemplary implementations relate to methods and apparatus for generatinggeological models with machine learning.

BACKGROUND

This section is intended to introduce various aspects of the art, whichmay be associated with exemplary embodiments of the present disclosure.This discussion is believed to assist in providing a framework tofacilitate a better understanding of particular aspects of the presentdisclosure. Accordingly, it should be understood that this sectionshould be read in this light, and not necessarily as admissions of priorart.

The upstream oil and gas industry explores and extracts hydrocarbons ingeological reservoirs which are typically found thousands of metersbelow the Earth's surface. Various types of geophysical and geologicaldata are available to characterize the subsurface, including seismicdata, well logs, petrophysical data, geomechanical data. In addition,various geological concepts, including environment of depositions (e.g.,channel or turbidities complexes, etc.) are available. Further, variousreservoir stratigraphic configurations, such as the number of channels,channel thicknesses, etc., may be inferred. The geophysical data, thegeological concepts, and the reservoir stratigraphic configurations maybe used to generate a reservoir model (or interpret one or morestratigraphic features), which in turn may be used to infer the valuesof their geological properties (e.g., Vshale, porosity, net-to-gross,etc.). These maps (or images) are then examined and interpreted with agoal of identifying geologic formations that may contain hydrocarbons(e.g., those formations are often referred as prospects when certaincriteria are met). The geologic details within those prospects maydelineate reservoirs and fluid contacts (e.g., contact surfaces betweenwater and oil legs) and may also be used for planning reservoirdepletion (including enhanced oil recovery (EOR)) and management.

Reservoir modeling (and stratigraphic interpretation) involvesconstructing a digital representation of hydrocarbon reservoirs orprospects that are geologically consistent with all availableinformation. The available information typically include: a structuralframework extracted from the seismic data (e.g., horizons, faults andboundaries describing a geobody or geobodies containing hydrocarbons);internal architecture (e.g., depositional facies or sequences); welllogs; petrophysics; and geological concepts associated with theenvironment of deposition (EOD). Geologic concepts (also interchangeablyreferred to as conceptual geological templates) and prior subsurfaceknowledge play an important role in reservoir modeling (andstratigraphic interpretation) when geologists and reservoir modelersattempt to predict the spatial heterogeneity of geological formationsbetween wells based on available sparse or incomplete data in 3D.Examples of the geological concepts (or EODs) are fluvial depositionalsystems, such as meandering or braided channel systems or turbidities.

Thus, 3D seismic provides a structural framework to extrapolate thespatial distribution of lithology and petrophysical properties beyond anappraisal (or analog) well locations. A set of key seismic informationused in reservoir modeling is illustrated in diagram 100 of FIG. 1 . Theinformation flow from seismic (and other geophysical data) to reservoirmodeling may be as follows:

(i) seismic data 110 is processed to generate a geophysical model 120,which may define one or more geophysical properties (e.g., compressionaland shear wave velocities, density, anisotropy and attenuation) of thesubsurface.

(ii) subsurface images, such as seismic images 130, are constructed,typically using the seismic reflection events and the invertedgeophysical models (e.g., velocity model) to migrate the events fromsurface locations to their subsurface locations. These images describethe reflectivity of subsurface boundaries between formations.

(iii) petrophysical properties, such as reservoir properties 150 (e.g.,porosity, permeability, and lithology), of the prospects are estimatedfrom the geophysical models, images and empirical petrophysical models(or rock physics model) along with available log data (appraisal oranalog wells).

(iv) all information is integrated with a reservoir framework 140,geologic concepts, such as EODs, to build one or more plausiblereservoir models 160. The properties in these reservoir models may bepopulated through geostatistical (e.g., kriging) or deterministicapproaches, which may be based on computational stratigraphy such asdepositional process simulations. The process based geologic simulationsmay be described by physical laws that govern the transportation ofsource materials, the deposition and compaction of rocks, and theirerosion. Reservoir geomechanics and tectonics (e.g., faulting, folding,unfaulting, unfolding or flattening) are also considered during thisprocess.

The constructed reservoir models may be later conditioned 170 to complywith seismic data by adjusting their geological parameters or reservoirstratigraphic configurations (e.g., thicknesses of the channels, numberof channels stacked in the reservoir, and channel paths). Seismicconditioning is complicated due to the manual adjustment of thegeological parameters, complexity of reservoir models, workflows, andcycle time.

An example reservoir modeling workflow 200 is illustrated in FIG. 2 .First, at 210, reservoir surfaces such as faults and horizonscorresponding to the interfaces of different formations (alsocorresponding to the instantaneous record of geological time) areinterpreted. Then, at 220, a watertight framework is obtained bydetermining the point of contact between horizons and the faults andintersecting them. Thereafter, at 230, the horizons are unfaulted andunfolded to an isochronal geologic state which corresponds to thegeologic horizon of the same age. Next, at 240, the horizons becomeuseful for stratigraphic modeling, such as interpreting stratigraphicfeatures. Depending on the geologic concepts associated with EODs (e.g.,confined channel systems), stratigraphic details conforming to theisochronal horizons are filled in. At 250, the stratigraphic model inthe isochronal state are deformed through folding and faulting processesto return to the current reservoir state or configuration, which isreferred as the geological model, such as the reservoir model. In theexploration stage, stratigraphic interpretation is used to create ageologic realization (which is often coarse and less detailed due to thelack of information which are available during development andproduction stages) of the target subsurface section similar to reservoirmodeling with less information. Hereafter, stratigraphic models may bereferred to as the reservoir models as well.

In this regard, stratigraphic interpretation and reservoir modeling area laborious, subjective, inconsistent and multi-disciplinary series oftasks, often leading to a suboptimal integration of all availableinformation.

SUMMARY

A machine learning method for generating one or more geological modelsof a subsurface is disclosed. The method includes: accessingconditioning data related to the subsurface; accessing one or moregeological concepts related to a target subsurface; accessing one ormore input geological models of the subsurface; training machinelearning model using the conditioning data, the one or more geologicalconcepts, and the one or more input geological models; and generating,based on the machine learning model, one or more geological models withnew conditioning data.

DESCRIPTION OF THE FIGURES

The present application is further described in the detailed descriptionwhich follows, in reference to the noted plurality of drawings by way ofnon-limiting examples of exemplary implementations, in which likereference numerals represent similar parts throughout the several viewsof the drawings. In this regard, the appended drawings illustrate onlyexemplary implementations and are therefore not to be consideredlimiting of scope, for the disclosure may admit to other equallyeffective embodiments and applications.

FIG. 1 is a flow diagram from seismic to simulations for buildingreservoir models.

FIG. 2 is an example reservoir modeling workflow.

FIG. 3 is a flow diagram for iteratively generating multiple geologicalmodels using machine learning.

FIG. 4 is a flow diagram for generating geological models using agenerative adversarial network.

FIG. 5 is a flow diagram for analyzing the generated geological modelsin order to characterize uncertainty.

FIG. 6A is a first example block diagram of a conditionalgenerative-adversarial neural network (CGAN) schema.

FIG. 6B is a second example block diagram of a CGAN schema.

FIG. 7 is block diagram of an architecture of a generative model basedon U-net architecture.

FIG. 8 is block diagram of an architecture of discriminator model whichresembles an image classification architecture.

FIG. 9 illustrates a first set of the interpreted surfaces, horizon andfault surfaces and automatically-generated reservoir model using theconditioned generative-adversarial networks trained with the SEAMFoothill geological data.

FIG. 10 illustrates a second set of the interpreted surfaces, horizonand fault surfaces and automatically-generated reservoir model using theconditioned generative-adversarial networks trained with the SEAMFoothill geological data.

FIG. 11 is a diagram of an exemplary computer system that may beutilized to implement the methods described herein

DETAILED DESCRIPTION

The methods, devices, systems, and other features discussed below may beembodied in a number of different forms. Not all of the depictedcomponents may be required, however, and some implementations mayinclude additional, different, or fewer components from those expresslydescribed in this disclosure. Variations in the arrangement and type ofthe components may be made without departing from the spirit or scope ofthe claims as set forth herein. Further, variations in the processesdescribed, including the addition, deletion, or rearranging and order oflogical operations, may be made without departing from the spirit orscope of the claims as set forth herein.

It is to be understood that the present disclosure is not limited toparticular devices or methods, which may, of course, vary. It is also tobe understood that the terminology used herein is for the purpose ofdescribing particular embodiments only, and is not intended to belimiting. As used herein, the singular forms “a,” “an,” and “the”include singular and plural referents unless the content clearlydictates otherwise. Furthermore, the words “can” and “may” are usedthroughout this application in a permissive sense (i.e., having thepotential to, being able to), not in a mandatory sense (i.e., must). Theterm “include,” and derivations thereof, mean “including, but notlimited to.” The term “coupled” means directly or indirectly connected.The word “exemplary” is used herein to mean “serving as an example,instance, or illustration.” Any aspect described herein as “exemplary”is not necessarily to be construed as preferred or advantageous overother aspects. The term “uniform” means substantially equal for eachsub-element, within about ±10% variation.

The term “seismic data” as used herein broadly means any data receivedand/or recorded as part of the seismic surveying process, includingparticle displacement, velocity and/or acceleration, pressure and/orrotation, wave reflection, and/or refraction data. “Seismic data” isalso intended to include any data (e.g., seismic image, migration image,reverse-time migration image, pre-stack image, partially-stack image,full-stack image, post-stack image or seismic attribute image) orproperties, including geophysical properties such as one or more of:elastic properties (e.g., P and/or S wave velocity, P-Impedance,S-Impedance, density, attenuation, anisotropy and the like); andporosity, permeability or the like, that the ordinarily skilled artisanat the time of this disclosure will recognize may be inferred orotherwise derived from such data received and/or recorded as part of theseismic surveying process. Thus, this disclosure may at times refer to“seismic data and/or data derived therefrom,” or equivalently simply to“seismic data.” Both terms are intended to include bothmeasured/recorded seismic data and such derived data, unless the contextclearly indicates that only one or the other is intended. “Seismic data”may also include data derived from traditional seismic (i.e., acoustic)data sets in conjunction with other geophysical data, including, forexample, gravity plus seismic; gravity plus electromagnetic plus seismicdata, etc. For example, joint-inversion utilizes multiple geophysicaldata types.

The terms “velocity model,” “density model,” “physical property model,”or other similar terms as used herein refer to a numericalrepresentation of parameters for subsurface regions. Generally, thenumerical representation includes an array of numbers, typically a 2-Dor 3-D array, where each number, which may be called a “modelparameter,” is a value of velocity, density, or another physicalproperty in a cell, where a subsurface region has been conceptuallydivided into discrete cells for computational purposes. For example, thespatial distribution of velocity may be modeled using constant-velocityunits (layers) through which is ray paths obeying Snell's law can betraced. A 3-D geologic model (particularly a model represented in imageform) may be represented in volume elements (voxels), in a similar waythat a photograph (or 2-D geologic model) is represented by pictureelements (pixels). Such numerical representations may be shape-based orfunctional forms in addition to, or in lieu of, cell-based numericalrepresentations.

Subsurface model is a model (or map) associated with the physicalproperties of the subsurface (e.g., geophysical or petrophysical models)

Geophysical model is a model associated the geophysical properties ofthe subsurface (e.g., wave speed or velocity, density, attenuation,anisotropy).

Petrophysical model is a model associated the petrophysical propertiesof the subsurface (e.g., saturation, porosity, permeability,transmissibility, tortuosity).

Geophysical data is the data probing the geophysical properties of thesubsurface (e.g., seismic, electromagnetic, gravity).

Geological model is a spatial representation of the distribution ofsediments and rocks (rock types) in the subsurface.

Reservoir model is a geological model of the reservoir.

Stratigraphic model is a spatial representation of the sequences ofsediment and rocks (rock types) in the subsurface.

Reservoir (structural) framework is the structural analysis of reservoirbased on the interpretation of 2D or 3D seismic images. For examples,reservoir framework comprises horizons, faults and surfaces inferredfrom seismic at a reservoir section.

Conditioning data refers a collection of data or dataset to constraint,infer or determine one or more reservoir or stratigraphic models.Conditioning data might include geophysical models, petrophysicalmodels, seismic images (e.g., fully-stacked, partially-stacked orpre-stack migration images), well log data, production data andreservoir structural framework.

Machine learning is a method of data analysis to build mathematicalmodels based on sample data, known as training data, in order to makepredictions and or decisions without being explicitly programmed toperform the tasks.

Machine learning model is the mathematical representation of a process,function, distribution or measures, which includes parameters determinedthrough a training procedure.

Generative network model (also referred as a generative network to avoidthe ambiguity with subsurface models) is an artificial network thatseeks to learn/model the true distribution of a dataset giving it theability to generate new outputs that fit the learned distribution.

Parameters of (generative or discriminator) network are weights orparameters of the neural or convolutional networks, which may bedetermined through training process.

Hyper-parameters of network are the parameters defining the architectureof the network/model (e.g., number of filters in the convolutionalneural networks, number of layers, convolutional filter sizes), theparameters defining training process (e.g., learning rate), which may bedetermined manually or using a reinforcement learning or Bayesianoptimization method.

Training (machine learning) is typically an iterative process ofadjusting the parameters of a neural network to minimize a loss functionwhich may be based on an analytical function (e.g., binary crossentropy) or based on a neural network (e.g., discriminator).

Objective function (a more general term for loss function) is a measureof the performance of a machine learning model on the training data(e.g., binary-cross entropy), and the training process seeks to eitherminimize or maximize the value of this function.

Adversarial training process for generative networks is a trainingprocess where the overall objective function that is being minimized ormaximized includes a term related to the objective function of anadversary, also termed a discriminator. In this process both thegenerator and discriminator are typically trained alongside each other.

Generative Adversarial Network (GAN) is an artificial network systemincluding generator (or interpreter) and discriminator network used fortraining the generative network model.

As used herein, “hydrocarbon management” or “managing hydrocarbons”includes any one or more of the following: hydrocarbon extraction;hydrocarbon production, (e.g., drilling a well and prospecting for,and/or producing, hydrocarbons using the well; and/or, causing a well tobe drilled, e.g., to prospect for hydrocarbons); hydrocarbonexploration; identifying potential hydrocarbon-bearing formations;characterizing hydrocarbon-bearing formations; identifying welllocations; determining well injection rates; determining well extractionrates; identifying reservoir connectivity; acquiring, disposing of,and/or abandoning hydrocarbon resources; reviewing prior hydrocarbonmanagement decisions; and any other hydrocarbon-related acts oractivities, such activities typically taking place with respect to asubsurface formation. The aforementioned broadly include not only theacts themselves (e.g., extraction, production, drilling a well, etc.),but also or instead the direction and/or causation of such acts (e.g.,causing hydrocarbons to be extracted, causing hydrocarbons to beproduced, causing a well to be drilled, causing the prospecting ofhydrocarbons, etc.). Hydrocarbon management may include reservoirsurveillance and/or geophysical optimization. For example, reservoirsurveillance data may include, well production rates (how much water,oil, or gas is extracted over time), well injection rates (how muchwater or CO₂ is injected over time), well pressure history, andtime-lapse geophysical data. As another example, geophysicaloptimization may include a variety of methods geared to find an optimummodel (and/or a series of models which orbit the optimum model) that isconsistent with observed/measured geophysical data and geologicexperience, process, and/or observation.

As used herein, “obtaining” data generally refers to any method orcombination of methods of acquiring, collecting, or accessing data,including, for example, directly measuring or sensing a physicalproperty, receiving transmitted data, selecting data from a group ofphysical sensors, identifying data in a data record, and retrieving datafrom one or more data libraries.

As used herein, a “gather” refers to a display of seismic traces thatshare an acquisition parameter. For example, a common midpoint gathercontains traces having a common midpoint, while a common shot gathercontains traces having a common shot.

As used herein, terms such as “continual” and “continuous” generallyrefer to processes which occur repeatedly over time independent of anexternal trigger to instigate subsequent repetitions. In some instances,continual processes may repeat in real time, having minimal periods ofinactivity between repetitions. In some instances, periods of inactivitymay be inherent in the continual process.

If there is any conflict in the usages of a word or term in thisspecification and one or more patent or other documents that may beincorporated herein by reference, the definitions that are consistentwith this specification should be adopted for the purposes ofunderstanding this disclosure.

As discussed above, understanding the subsurface and the fluids thereinis important to all stages of the upstream workflows. There are twoapproaches to improving the understanding of the subsurface including:(1) acquiring additional data regarding the subsurface, which may beprohibitively expensive; or (2) better managing the existing dataobtained through understanding the range of plausible potentialsubsurface realities that are consistent with some or all availabledata. The latter option may be achieved by generating geological models(such as reservoir or stratigraphic models) with varying structuralframeworks, reservoir properties, architecture with suitable parametricvariations and alternative geologic templates based on environments ofdepositions (e.g., channel systems, carbonate systems, alluvialsystems). In one implementation, the geological models, includingreservoir modeling and stratigraphic interpretation methods, areautomatically generated based on machine learning, such as deepgenerative networks.

As discussed above, stratigraphic interpretation and reservoir modelingare labor-intensive and becomes increasingly complex as the complexityof reservoirs and prospects increases. Automating reservoir modeling,which may consider multiple scenarios without sacrificing the geologicalquality, may augment seismic interpretation and reservoir modeling todevelop and manage hydrocarbon reservoirs. For example, sedimentationmay vary, leading to different modalities of geologies, with the seismicdata (such as the field seismic data) lacking sufficient resolution todefinitively indicate a particular modality. Thus, the machine learningmay generate a plurality of reservoir models that account for differentsedimentation and different modalities of geologies that comport withthe seismic data. In this regard, automating reservoir modeling mayaddress one, some or all of the following challenges with typicalreservoir modeling methods including: availability of reservoir modelsfor exploration; bias; time-intensive manual process; seismic,geophysical and petrophysical conditioning; and reservoir productionhistory matching.

With regard to the availability of reservoir models for exploration,exploration decisions are typically made with rudimentary assumptionsregarding reservoir geology, which may be based on geologists' sketches.Because stratigraphic analysis is a laborious task and has beendifficult to translate into computer instructions to automate theprocess, only one stratigraphic model is usually provided to makedecisions without fully understanding uncertainties associated withreservoir geology. Automatically generating a set of plausiblerealizations (such as an ensemble) of reservoir models via machinelearning during one or more stages of exploration may be valuable inorder to make rapid and risk-aware decisions.

With regard to bias, interpretation of stratigraphy and the constructionof reservoir models with incomplete and erroneous data may be anidiosyncratic and exhaustive process based on a particular geologist'sprior training and experience. This may lead to a biased view on theinstantiations of geological scenarios, partially when the geology iscomplex. Automatically generating reservoir models may alleviate thissubjectivity in the process in order to appreciably quantify uncertaintyin the generated reservoir models.

With regard to the time-intensive nature of the typical process,stratigraphic interpretation and reservoir model building processes arebased on laborious tasks, as discussed above. Automating these processesusing machine learning may significantly accelerate exploration,development and recovery of hydrocarbon reservoirs.

With regard to seismic and petrophysical conditioning, the reservoirmodels are typically created only using interpreted surfaces andgeological concepts. Later, these created models are modified to honorseismic and petrophysical data. This serial process of creating themodels and thereafter modifying the models to comport with the availabledata presents a challenge because the parameters manipulating thesemodels are manually determined, discontinuous and highly nonlinear.Integrating the creation of the reservoir models and the comportmentwith the seismic and petrophysical data may eliminate these additionalconditioning tasks.

With regard to reservoir production history matching, in the presence ofproduction data, scenario-based reservoir models are recalibrated withthe production data to narrow the range of parameters in each scenarioor eliminate impractical ones. However, because the number of uncertainreservoir parameters are usually large and nonlinearly related (e.g.,any one parameter may depend on the value of the others), typicalworkflows, which depend on manually or assisted history matchingapproaches, are lacking. In contrast, machine learning may automaticallygenerate multiple potential reservoir modes conditioned with theproduction data along with all the prior data.

Thus, in some implementations, machine learning generates one or moregeological models, such as one or more reservoir models or one or morestratigraphic models that are consistent with applicable geologicalconcepts and/or conditioning data (e.g., seismic and other availableinformation useful to infer the plausible reservoir geology). Inparticular, machine learning may generate reservoir models (or interpretstratigraphy) that are automatically conditioned with any one, anycombination, or all of: (1) seismic data; (2) interpreted surfaces; (3)geobodies; (4) petrophysical/rock physics models; (5) reservoir propertymodels; (6) well log data; and (7) geological concepts.

Various types of machine learning methodologies are contemplated,including generative-model-based, image-to-image-translation-based,style-transfer-based, clustering-based, classification-based, orregression-based machine learning. Also, various types of learningparadigms are contemplated, including supervised, semi-supervised,unsupervised, reinforcement, or transfer learning paradigms. As merelyone example, a generative adversarial network (GAN) may be used as themachine learning methodology. In one implementation of GAN, two neuralnetworks, including a generative network (which generates candidatereservoir models) and a discriminative network (which evaluates orclassifies the candidate reservoir models), contest with each other.Given a training set, such as a collection of previously constructedreservoir models (manually or using existing workflows), the GAN maylearn to generate one or more candidate reservoir models, such as asingle reservoir model or a plurality of reservoir models. For example,the GAN may generate multiple scenarios of reservoir models based on oneor more of: (1) the geological concepts; and (2) structuralconfigurations (e.g., whether a fault is present or not). As discussedfurther below, the training of the GAN may be unconditioned orunsupervised (e.g., where the model is trained to generate realisticimages from scratch, such as by inputting random noise), or conditionedor supervised (e.g., in addition to inputting random noise, the networkis given “conditions” to encourage it to create realistic images thatare also consistent with some structure, such as structural framework orseismic data or petrophysical data or log data).

The GAN may receive various inputs, such as any one, any combination, orall of: conditioning information; latent code; or noise to generate arealization of the reservoir geology. Further, in one implementation,the GAN may generate the multiple reservoir models using one or morefixed inputs (such as the seismic image) and other varying inputs (suchas the latent code and/or the noise).

The generative model may learn a relationship between noises and/orlatent codes (if enforced) inputted to the generative model andstratigraphic configurations (e.g., channel thickness in channel systemconcepts) of a reservoir model outputted by the generative model. Thismay eliminate an effort required for the state-of-the-art reservoirmodeling approaches for the explicit parameterization of stratigraphicconfigurations (e.g., a parameter controlling a channel thicknesses inthe channel system concepts).

In this regard, various inputs to the GAN are contemplated as trainingsets. According to some embodiments, synthetically-generated geologicalmodels (such as synthetically generated reservoir models) and thecorresponding simulated or field seismic data and/or the petrophysicaldata associated with the seismic data may be used as a training set forthe GAN. For example, reservoir models, such as existing reservoirmodels or previously GAN-generated reservoir models, may be conditionedby the GAN to comport with the specific conditions at hand, such as thespecific seismic data which may be partially-stacked or pre-stack data,or may be conditioned to honor petrophysical data, log data, andnet-to-gross expectations. As another example, the reservoir modelsinput to the GAN for training a generative network need not beconditioned (e.g., cycle GANs which do not require conditioning datapaired with the reservoir models). Further, simulation methods (e.g.,discretization methods for solving partial differential equationsgoverning a physical phenomenon) may be used to generate syntheticseismic data, and petrophysical models or rock physics models togenerate synthetic logs and petrophysical property maps for a givenreservoir model. In this way, the reservoir model will automatically beconditioned to the all data simulated. In turn, thesesynthetically-generated data paired with the reservoir models may beused to train the generative models.

According to the foregoing and/or various other embodiments,stratigraphic sketches and the corresponding simulated or field seismicdata and/or the petrophysical data associated with the seismic data maybe used as a training set. Stratigraphic sketches may comprisediagrams/models that depict the distribution of lithologies, facies orvarious rock types related to particular EODs. These sketches may beconstructed to convey the spatial distribution of rock types or bulkproperties, such as porosity. For example, the location of geologicfeatures of interest, such as channel fill (e.g., potential reservoirrock), may be inferred through integration of interpretation of seismicdata when considering observations made from field studies (e.g.,outcrops) or analogues. Such geologic features may be portrayed orsketched by a mask capturing a realization of the geological context.

In some embodiments, computational stratigraphy (such as based onsedimentation/transportation laws expressed by partial differentialequations) may be used to generate stratigraphic or reservoir models andseismic simulations and/or the petrophysical models may be used togenerate seismic and/or petrophysical data associated with thosesynthetic stratigraphic or reservoir models. Such synthetic reservoir orstratigraphic models along with seismic and petrophysical data may be asa training set. In particular, computational stratigraphy comprises anumerical approach to simulate sediment transport. Using rock physicsmodels, outputs of computational stratigraphy simulations may beconverted to maps of geophysical properties, such as velocity anddensity. These geophysical properties may in turn be used to generatesynthetic seismic data. The generative models may thus be trained withthese geological models constructed with computational stratigraphysimulations and their synthetic seismic data.

In various embodiments, the generated geological models are analyzed forat least one aspect (e.g., uncertainty). As one example, the generatedgeological models are analyzed for uncertainty in net-to-gross ratio(e.g., fraction of sand thickness with respect to the total depositionalunit thickness at the reservoir section). In particular, uncertaintyassociated with one or more reservoir models may assist in hydrocarbonexploration, reservoir development and depletion decisions. As anotherexample, the generated geological models are analyzed for uncertainty asto EODs, whereby multiple EOD concepts may be considered (e.g., confinedchannel system versus weakly confined channel system hypothesis may betested). This differentiation may have a significant impact to thereservoir geology and fluid in pore space distribution, such as tonet-to-gross, and fluid volume and flow, and thus the depletionplanning. As discussed further below, generative networks may be used totest these multiple scenarios in the process of generating anddiscriminating multiple potential reservoir models, giving additionalcontrol to test geologic concepts directly from data, thereby markedlyimproving the value of the various case studies that are typicallycreated to act as an informational aid. For example, during GANtraining, a section from the mask volume may be extracted. There may bemultiple potential concepts (e.g., different potential geologicaltemplates) associated with the extracted section. The instantiations ofthe reservoir models from these multiple potential concepts in theextracted section may be isolated and input to the GAN along with itsconditioning data in order to train the generative network. Suchtraining will enable the generative network to learn reservoir featuresor patterns that correspond with the particular concept. In this way,the GAN may process different sections of the subsurface in order toanalyze the potential universe of geological structures and how theycomport with the given data.

Traditionally, a single reservoir model or a very limited set ofreservoir models (e.g., high-mid-low reservoir models) are used,providing a very limited ability to quantify uncertainty and forecastvariabilities in reservoir performance. In contrast, an automatedreservoir modeling methodology conditioned with all available data mayassist in characterizing full complexity of the reservoir uncertainty,and may capture scenarios representing the reservoir uncertainty.Various approaches to uncertainty are contemplated, such as afrequentist approach based on a sampling distribution and a Bayesian orprobabilistic approaches (sampling methods (e.g., importance sampling),perturbation methods (e.g., local expansion technique),functional-expansion methods (e.g., polynomial chaos expansion),numerical integration methods) estimating the reservoir posteriordistribution given a prior distribution of key parameters (e.g.,structural variability, geological concepts or a set of learnedparameters such as the latent variables learned by a variationalautoencoder). Other uncertainty methodologies are contemplated.

Multiple realizations of the reservoir models, which may be generated bythe generative network, may thus be used to estimate the statisticaldistributions of the target reservoir quantities which may include anyone, any combination, or all of: net-to-gross; spatial continuity (e.g.,reservoir connectivity/heterogeneity measures affecting tortuosity);distribution of dynamic properties affecting fluid flow conditions; ordistribution of petrophysical properties.

Referring to the figures, FIG. 3 is a flow diagram 300 for generatingmultiple geological models using machine learning at one or more stagesof the life cycle of oil and gas field (e.g., exploration, developmentand production). For example, machine learning may be used in any one,any combination, or all of: the petroleum exploration stage; thedevelopment stage; or the production stage. Exploration may include anyone, any combination, or all of: analysis of geological maps (toidentify major sedimentary basins); aerial photography (identifypromising landscape formations such as faults or anticlines); or surveymethods (e.g., seismic, magnetic, electromagnetic, gravity,gravimetric). For example, the seismic method may be used to identifygeological structures and may rely on the differing reflectiveproperties of soundwaves to various rock strata, beneath terrestrial oroceanic surfaces. An energy source transmits a pulse of acoustic orelastic energy into the ground which travels as a wave into the earth.At each point where different geological strata exist, a part of theenergy is transmitted down to deeper layers within the earth, while theremainder is reflected back to the surface. The reflected energy maythen be sensed by a series of sensitive receivers called geophones orseismometers on land, or hydrophones submerged in water. Similarly,additional data may be generated in each of the subsequent stages ofexploration; development (e.g., new densely-acquired broadband 3Dseismic, well logs) or production (e.g., 4D or time-lapse seismic formonitoring reservoir).

At 310, various conditioning data, available for a respective stage ofthe life cycle of an oil and gas field and for use as input to thegenerative network, may be accessed. The life cycle of the oil and gasfield may include any one, any combination, or all of: exploration;development; or production. As discussed above, various types ofgeophysical data (e.g., seismic data), various geological concepts(e.g., reservoir geological concepts, EODs or other concepts derivedfrom experience or from the data), a set of interpreted surfaces (e.g.,horizons or faults) or zones (e.g., strata, anticline structure andreservoir section), and various reservoir stratigraphic configurations(e.g., lithofacies learned from the well logs) may be used. In some orall embodiments, all of the available conditioning data relevant to thereservoir (or the target subsurface area) may be the input to apreviously trained generative model to generate one or more geologicalmodels in the respective stage. For example, in the exploration stage,one, any combination, or all of the following may comprise availableconditioning data: seismic images (e.g., measured and/or simulated);geophysical models (e.g., velocity model, density model); petrophysicalmodels (porosity model; permeability model; estimates of sand and shalefacies; etc.); structural framework constructed using the interpretedsurfaces; and geological concepts (e.g., the identified EOD (or othergeological template)). As another example, in the development stage,one, any combination, or all of the following may comprise availableconditioning data: all data available in the exploration stage (e.g.,exploration data); seismic data generated in the development stage; andwell data. As still another example, in the production stage, one, anycombination, or all of the following may comprise available inputs: alldata available in the exploration stage (e.g., exploration data); alldata available in the development stage (e.g., development data);pressure tests; production data; and 4D seismic (see e.g., US PatentApplication Publication No. 2018/0120461 A1, incorporated by referenceherein in its entirety).

At 320, machine learning is performed using the accessed data in orderto train a machine learning model. At 330, one or more geological modelsfor the respective stage of the life cycle are generated based on themachine learning model. At 340, it is determined whether to continuemachine learning. If not, flow diagram 300 ends. If not, at 350, it isdetermined whether to resample the current conditioning or training dataor leverage additional conditioning or training data (such as data froma next stage of the life cycle of oil and gas exploration/production) ifavailable. If so, flow diagram 300 loops back to 310 as shown by line360. Specifically, line 360 is illustrated as a dashed line to indicatethat an iterative process of flow diagram 300 for the different stagesof the life cycle is optional.

In this regard, the machine learning methodology may generate multiplegeological models that comport with applicable geological concepts andwith all available conditioning data (including the data informative ofgeology from the latest stage of exploration, development or production)and geological concepts. In some embodiments, the sequence of blocks 310and 320 for a respective stage is independent of the sequence of blocks310 and 320 for other stages of the life cycle of oil and gas field.Specifically, the inputs to block 310 and the machine learning performedat block 320 in order to train the machine learning model for arespective stage is independent of inputs/machine learning for otherstages of the life cycle. Alternatively, one or both of the inputs toblock 310 or the machine learning performed at block 320 in order totrain the machine learning model for a respective stage may be dependenton the inputs and/or machine learning (including the machine learningmodel in the previous stage) for another stage of the life cycle. As oneexample, outputs from a previous iteration, such as one or morereservoir models or scenarios, may be used as input for a subsequentiteration. As another example, machine learning performed in a previousiteration, used to train the machine learning model in the previousiteration, may be used in part or in whole for a subsequent iteration(e.g., the generative network trained in a previous iteration may beused as a basis for the generative network in a subsequent iteration).In particular, responsive to acquiring additional data, the system maycontinue training (or re-training) the existing generative network orexpand the existing generative network (e.g., increasing number offilters in a layer or adding new layers) in order to incorporate theadditional data. In some embodiments, an existing and previously-trainedgenerative network may be expanded with additional layers and itsexpanded part may be only trained with the additional data while thepreviously-trained part of the generative network is fixed (e.g., nottrained). This may also be referred as a transfer learning where theprevious-learnings are transfer to the new expanded model while new datais incorporated in the generative network. In some embodiments, theexpanded generative network can be trained or re-trained as whole (allparameters of the generative network are updated during the training orre-training).

For example, a first sequence of flow diagram 300 (e.g., a firstiteration) may be performed responsive to the exploration stage in whicha set of applicable geophysical data and a set of applicable geologicalconcepts are used by the machine learning methodology in order togenerate the geological models (e.g., a first plurality of reservoirmodels). In particular, the applicable geological and geophysical datamay comprise seismic data generated from exploration surveying andsimulated seismic data generated by geological models of sites similarto the current site. Further, the applicable conditioning data maycomprise any one, any combination, or all of: the structural framework(e.g., horizons, faults and boundaries describing a geobody or geobodiescontaining hydrocarbons); internal architecture (e.g., depositionalfacies or sequences); petrophysical property models (e.g., porosity,permeability, and lithology); or geological concepts associated with theenvironment of deposition (EOD). The applicable geological concepts maycomprise values (or ranges of values) or may comprise different types(e.g., confined channel systems) and may be selected as potentiallydescribing the subsurface based on the current applicable data.Thereafter, responsive to obtaining additional data responsive toreservoir development, an updated set of applicable conditioning data(e.g., second stage data) may be used in addition to the available priorconditioning data from exploration stage by the machine learningmethodology in order to generate the geological models (e.g., a secondplurality of reservoir models which is different from the firstplurality of reservoir models or which are subset of the first pluralityof reservoir models because not all of the first plurality models areconsistent with the new conditioning data). The updated set ofapplicable conditioning data may include the additional data obtainedduring reservoir development phase. Further, the updated set ofapplicable geological concepts may reflect additional informationobtained during development phase, potentially revising the values (ornarrowing the ranges of reservoir models or reservoir values) or maycomprise different types from the set of applicable geological conceptsgenerated from exploration phase. In this way, responsive to additionalinformation, the inputs to the machine learning methodology mayiteratively generate geological models to comport with the latestconditioning data including new geophysical or petrophysical, reservoirframework or well data.

As discussed above, various machine learning methodologies arecontemplated. As one example, a generative adversarial network (GAN) maybe used, such as illustrated in FIGS. 6A-B. In this regard, anydiscussion regarding the application of GAN to generate and/or evaluategeological models may likewise be applied to other machine learningmethodologies.

Specifically, FIG. 6A is a first example block diagram 600 of aconditional generative-adversarial neural network (CGAN) schema in whichthe input to the generative model G (630) is conditioning data (e.g.,geophysical data, petrophysical data and structural framework) x (610)and noise z (620). FIG. 6B is a second example block diagram 660 of aCGAN schema in which the input to the generative model G (680) isconditioning data x (610), noise z (620), and latent codes c (670).Other types of GANs are contemplated including deep convolutional GANs(DCGANs), Stacked Generative Adversarial Networks (StackGAN), InfoGANs(an information-theoretic extension to the GAN that is able to learndisentangled representations in an unsupervised manner), WassersteinGANs (where the loss function is changed to include a Wassersteindistance that correlates to image quality), Discover Cross-DomainRelations with Generative Adversarial Networks (Disco-GANS), or thelike. The impact of noise z can also be achieved through intermediatedropout layers within the generative network to induce stochasticbehavior to vary the diversity of generated output in models whereconditioning data x is provided. The noise distribution may also belearned as a prior distribution using a machine learning process such asa decoder (that learns a mapping from a latent space to the image space)or an autoencoder, or a variational autoencoder (VAE) or VAE-combinedGAN(VAEGAN) model.

GANs include generative models that learn mapping from one or moreinputs to an output (such as y, G: z→y where y is output (e.g.,reservoir model) and z is noise), through an adversarial trainingprocess. This is illustrated in FIG. 6A, with generative model G (630)outputting G(x, z) (640) and in FIG. 6B, with generative model G (680)outputting G(c, x, z) (690).

In this training process, two models may be trained simultaneously,including a generative model G (630, 680) and a discriminative model D(655, 695) that learns to distinguish a training output y (also calledreference output or ground truth) (650) from an output of generativemodel G (630, 680). On the other hand, generator G (630, 680) is trainedto produce outputs that cannot be distinguished from reference outputs y(650) by discriminator D (655, 695). This competition between G and Dnetworks may converge at a local Nash equilibrium of Game Theory (or GANconvergences when the D and G weights do not change more 1% of itsstarting weight values; weights are the D and G model parameters whichare updated during the training process based on an optimization methodsuch stochastic gradient method), and generative model G learns mappingfrom noise and input x providing conditions to output y, G: (x, z)→y.Thus, convergence may be defined in one of several ways, includingtopological convergence.

As shown in FIG. 6A, the generative model G may take x as input, whichmay include all available conditioning data at an upstream phase, suchas multiple seismic images (e.g., pre-stack images), interpretedsurfaces, or petrophysical property models, along with a noise array z.Alternatively, the noise array may be accompanied with a latent vector(or code) c, as illustrated in FIG. 6B. The latent code may be used toinstruct generative model G (680) to generate outputs (e.g., geologicalmodels, such as stratigraphic models or reservoir models) consistentwith a particular EOD system. As one example, a set of c values maygenerate outputs for channel systems and other values of c may result inoutputs suited for alluvial EOD systems. As another example, a set of cvalues may generate a variety of channel complexes (e.g., differentnumbers of channels, different channel thicknesses, etc.). In this way,a set of c values may be used to perturbate the generative model andfurther may be used to instruct the generative model to generate modelsin one or more types of clusters.

In some cases, the use of latent codes may be avoided by trainingseparate generative models, such as each being specialized to generateoutputs for a particular EOD. In this regard, multiple generative models(such as illustrated in FIG. 6A) may be used, with each respectivegenerative model associated with a different latent code.

The generative model may be based on a deep network, such as U-net, asillustrated in the block diagram 700 of FIG. 7 , in which an autoencoder(AE), variational autoencoder (VAE) or any other suitable network maps{x, z, c} to an output of stratigraphic or reservoir model. In cases ofAE or VAE, the generative model G may be split into encoder or decoderportions, with the decoder portion being used directly to generateoutputs after training is completed. The generative model G may betrained iteratively by solving an optimization problem which may bebased on an objective functional involving discriminator D and a measureof reconstruction loss (e.g., an indication of the similarity of thegenerated data to the ground truth) and/or adversarial loss (e.g., lossrelated to discriminator being able to discern the difference betweenthe generated data and ground truth).

Various weighting of the reconstruction loss and the adversarial lossare contemplated. In particular, the weight for each of thereconstruction loss and the adversarial loss may typically range between[0,1] where 0 eliminates the impact of that loss altogether duringtraining; however, the respective weight may exceed 1.0. As one example,initially, the reconstruction loss and the adversarial loss may beweighted equally at 1.0. For example:total_loss=(reconstruction_weight*reconstruction_loss)+(adversarial_weight*adversarial_loss).Thus, the individual losses may be a composite of other loss functions(e.g., the reconstruction loss may be L1 and L2 loss functionstogether). Further, a loss function measuring the mutual information ora lower bound to the mutual information between code c and reservoirmodels produced by the G may be used included in the training objectivefunction. A complete formula for the total loss may change between GANs(e.g., the loss formula used for the Conditional GAN may be differentfrom the loss formula used for the Style-GAN or Cycle-GAN).

The weights may be changed dependent on analysis of the trainingsequence. For example, If during training, it is determined that thediscriminator has become too powerful e.g., the generator is unable togenerate an output that fools the discriminator), the weight on theadversarial loss may be adjusted.

Thus, the weights may be selected dependent on desired quality of thegenerated outputs and the learning performance during training, asindicated by the loss function, for both the generator and discriminatornetworks. For example, in reservoir modeling, there are instances wherethe goal is to create as realistic of images as possible. In suchinstances, the weight may be adjusted. In other instances, the goal maybe to create diverse scenarios responsive to a specific set of inputs.In such instances where it is desired to create diverse scenarios, themachine learning may be modified in one of several ways. In one way, thereconstruction loss may be reduced so that the generated data does notnecessarily need conform perfectly to the input data. In another way,the dropout may be increased. Dropout may range from [0,1], withDropout==0 resulting in all of the information from the neurons in thenetwork will pass through the model and Dropout==0.5 resulting in arandom 50% of the information in the neurons will not pass through thatlayer of the network. Increasing the dropout may allow for diversescenario generation since for the same set of inputs, not all of thesame information will be sent through the network.

Referring back to the objective function, it may take the form of:F _(G)(W _(G))=

_(X,Z)[log(1−D(x,G(W _(G) ;x,z)))]+λ

_(X,Y,Z)[∥y−G(w _(G) ;x,z)∥]  (1)where y is one or more reference reservoir model, X, Y, Z arecollections of x, y and z inputs respectively,

_(X,Z) is the expectation of [ ] over all populations of x and z, W_(G)is the parameters (or weights) of generative model G to be determined byminizing F_(G), λ is the weighting factor between two objectives, and ∥∥ is a misfit norm such as L₁ or L₂. If latent code c is used forgenerating reservoir models, then G function takes the form of G(W_(G);c, x, z).

The output of generative model G (e.g., stratigraphic models orreservoir models), samples of reference stratigraphic models orreservoir models y, x and latent code c (if c is inputted to G, such asillustrated in FIG. 6B) may be input to decimator D. In oneimplementation, the output of D is a scalar typically ranging from 0 to1 indicating the discriminator's confidence as to whether it hasreceived generated data from G or ground truth data. Discriminator D maybe based on a deep network architecture, such as illustrated in theblock diagram 800 in FIG. 8 . The discriminator D may be trained with anobjective functional which may take the form of:F _(D)(W _(D))=

_(y)[log(D(W _(D) ;x,y))]+

_(x,z)[log(1−D(W _(D) ;x,G(x,z)))]  (2)where, W_(D) is the parameters of the discriminator to be determined bymaximizing F_(D). If the latent code c is used in generator G, then theD function may take the form of D (W_(D); c, x, y) or D(W_(D); c, x,G(x, z)).

Equations (1) and (2) may be iteratively solved in an alternatingfashion by repeating a number of iterations over (1) and then a numberof iterations over (2). A combined optimization problem may be expressedas:

$\begin{matrix}{G^{*} = {{\arg_{W_{G},W_{D}}\mspace{14mu}{\min\limits_{W_{G}}\mspace{14mu}{\max\limits_{W_{D}}\mspace{14mu} F_{D}}}} + F_{G}}} & (3)\end{matrix}$

Equation (3) may also be augmented with terms regulating parameters ofdiscriminator or generator, W_(D) or W_(G), or latent code space c. Forinstance, a mutuality measure (or a lower bound to the mutuality)between the latent code c and generator output G(x, z, c) may bemaximized to relate the latent code c with different output modalities(e.g., a set of c values generates outputs for the channel systems andanother set of c values may generate outputs suited for alluvial EODsystems). During the use of trained generators, different modalities ofoutputs may be constructed by choosing an appropriate latent code. Thisis discussed further below with regard to multi-scenario generation.

FIG. 4 is a flow diagram 400 for generating geological models using aGAN. As discussed above, the generative model G may receive variousinputs. In this regard, various inputs may be accessed such as any one,any combination, or all of the following: training reservoir models,stratigraphic sketches (e.g., diagrams/models) depicting thedistribution of lithologies, rock types and facies related to one ormore EODs or synthetic reservoir models produced using computationalstratigraphy simulations (410); these models may then be paired withfield data or these models may be used to produce conditioning datausing synthetic simulators (e.g., seismic wave simulators), (420);geophysical models (e.g., velocity and density models), petrophysicalmodels, seismic images, synthetic seismic images generated using seismicwave simulations (430); and noise inputs for a given set of conditions(440). For example, performing conditioning may comprise generatingconditioning data using real or synthetic simulators (e.g., seismicsimulator). The synthetically-generated conditioning data may then besupplemented (e.g., using style transfer methods such as Cycle-GAN) witha structured noise to reflect the real data challenges, as discussedfurther below.

At 450, a generative model is trained using all the accessed data. At460, the various inputs may be used in order to generate multiplegeological models using the trained generative model from 450. And, at470, the generated multiple geological models may be analyzed for atleast one aspect, such as uncertainty.

In some embodiments, synthetically-generated conditioning data (e.g.,seismic simulators) at 420 may further be manipulated or augmented witha structured noise to represent challenges in the field data. Forexample, a style transfer approach (e.g., Cycle-GAN) can learn totranslate synthetic data to field data by manipulating the syntheticdata style (e.g., frequency distributions) or by adding a noise whichhas a similar distribution encountered in the field data. Astyle-transfer approach may be selected from a plurality of styletransfer approaches, with the selection of the style-transfer approachbeing specific to a geological basin, data acquisition type (e.g.,marine versus land data acquisition or streamer versus nodal marineacquisitions) or processing workflows to account for the effects whichare not modeled with the simulators (e.g., the synthetically-generatedconditioning data is generated using one or more simulators, and thestyle transfer approach is selected to account for the effects notmodeled with the one or more simulators).

In one implementation, GANs may generate multiple output realizationsdepending on one or more inputs, such as with multiple noise inputs fora given set of conditions. In some applications, a dropout strategy maybe used during applications of the trained generator in order togenerate various output instantiations. Specifically, dropout mayrandomly deactivate or ignore a certain percentage or set of connectionsbetween neurons as data passes through the network.

As discussed above, noise may be input to the generative model G. Use ofnoise as an input to the generative model G may not be effective togenerate multi-scenario models, particularly when the scenarios areexpected to illustrate characteristic differences across the realizedoutputs. In such an instance, a latent code may also be input to thegenerative model G, whereby the GAN may be trained to maximize themutual information between the generated outputs and the codes. In oneimplementation, the latent code space may be structured using a prioriknowledge about the application. For instance, the latent code space maycomprise various ranges. In particular, generating differentinstantiations of integer numbers from 1 to 10, one latent code mayassume values 1 to 10 corresponding to integers to be generated. Forgenerating multi-scenario reservoir modes, it may be difficult tostructure such a latent space. Instead, AE or VAE may be trained inadvance to learn a latent space, which may then be used to structure thelatent code for generating imperative models and to learn a prioridistribution of these latent code space.

Additionally, style transfer methods may be leveraged to generatemulti-scenario models. The network designed for style transfer may betrained by incorporating content and style into the loss function. TheGAN may attempt to maintain the content of the original scenario whilealso honoring the style variant that is being applied to the scenario.

As discussed above, the generated geological models may be analyzed forassociated uncertainty. Reservoir uncertainty characterization may becomputationally feasible by deep generative models, which arecomputationally effective representation of the reservoir models with alow dimensional latent space. These generative models are fast toinstantiate reservoir models and compute the aforementioned targetreservoir quantitates. Some of the generative models, such as ones basedon VAEs, may inherent the prior distributions of the latent parametersto compute the posterior distributions of the target reservoirquantities of interest. The automated reservoir models discussed hereinmay use the conditioning information and a set of random latent codeand/or noise to generate a realization of the reservoir geology.Further, the conditioning information, such as the seismic image, may befixed and the only set of variables for generating different reservoirmodel scenarios may be the latent variables and/or noise. The targetreservoir quantities may be calculated based on the reservoirrealizations. In certain instances, multi-modal distributions may becharacterized by key scenarios and their local statistics representingeach modal distribution. In other cases, all possible realizations maybe clustered to identify characteristically dissimilar scenarios. Also,reservoir flow simulations including surrogate models based deep networkmodels may use the samples of reservoir models in order to estimateposterior distributions of dynamic reservoir properties or reservoirflow conditions (e.g., oil, gas and water production rates). As such,FIG. 5 is a flow diagram 500 for analyzing the generated geologicalmodels in order to characterize uncertainty. At 510, statisticaldistributions are estimated for the generated geological models based onone or more of the following: net-to-gross; spatial continuity;distribution of dynamic properties affecting fluid flow conditions; ordistribution of petrophysical properties. At 520, uncertaintycharacterization is performed to produce confidence intervals,inferential statistics using a frequentist inference or Bayesianinference, analyzing the estimated statistical distributions.

As discussed above, the disclosed methodology may be applied to avariety of instances. By way of example, the methodology is applied viaa synthetic dataset representative of geologic features found in regionsof active mountain building, such as sharp topography and alluvialdeposits resulting from rapid erosion at the surface, along with complexstructures resulting from compressive fold-and-thrust tectonics atdepth.

For illustrations of synthetic data sampled for training the GAN modelin accordance with this example, please see FIGS. 9(b) and 11(a) of C.Regone, J. Stefani, P. Wang, C. Gerea, G. Gonzalez, and M. Oristaglio,Geologic model building in SEAM Phase II—Land seismic challenges, TheLeading Edge, 2017 (hereafter referred to as “Regone et al. 2017”),which figures are incorporated herein by reference. FIG. 9(b) of Regoneet al. 2017 is an image of the SEAM (SEG Applied Modeling) Foothillsstructural framework interpreted from seismic images; and FIG. 11(a) ofRegone et al. 2017 is an image of a geological model (obtained from itscompressional velocity volume) based on the SEAM Foothills geologicalmodel (of Regone et al. 2017 FIG. 9(b)). FIG. 11(a) of Regone et al.2017 illustrates an instantiation of the geological model based on thestructural framework. Per the present example, the structural frameworkand its seismic image are sampled for training the GAN model. Thetraining outputs may comprise samples of geological models.

The structures in the framework may be uniquely labelled. To generate avariety of training examples, different sections may be extracted, suchas extracting a slice of the structural framework so that a top andbottom surface are randomly selected. The geological model may betrimmed at the corresponding locations. This provides the GAN with manydifferent examples of structural combinations. Optionally, dataaugmentation may be applied in order to recognize other plausiblesubsurface geometries which are not realized in the model, such asdiscussed in U.S. Patent Application No. 62/826,095, entitled DataAugmentation For Seismic Interpretation Systems And Methods (attorneyreference number 2019EM103), incorporated by reference herein in itsentirety. The augmentation strategy may manipulate the reservoir models,structural framework and seismic image samples by applying nonlineardeformations. The structural framework may contain different types ofsurfaces, such as horizons and faults. When the generative model isintroduced with the different types of surfaces, their unique labels mayeither be removed, maintained, or changed to provide additional contextto the model (e.g., fault surfaces may be labelled with a uniquedescriptor to assist the generator associate discontinuities on thesurfaces with the descriptor).

The generative model may process the conditioning data and noise, andoutput one or more reservoir models with geological details consistentwith its training geological concept (e.g., alluvial system) to fill inreservoir framework. The output of the generative model is thus passedto discriminator in order for the discriminator to evaluate itsacceptance as a reservoir model. As discussed above, the discriminatoris also provided with real reservoir samples extracted from thegeological model. The discriminator may therefore attempt to discernwhich it considers as real and which it considers as fake. At each stepof the training, the generator and/or the discriminator have a chance tolearn and update their respective models. The generative model accuracyis measured by the training and validation losses along with outputtingresults throughout the training to inspect visually.

FIGS. 9 and 10 illustrate respective sets of the interpreted surfaces,horizon and fault surfaces and automatically-generated reservoir modelusing the generative networks trained with the SEAM Foothill geologicaldata. In the examples illustrated in FIGS. 9 and 10 , the structuralframeworks are extracted from the structural framework shown in FIG.9(b) of Regone et al. 2017, and manipulated to represent unseenstructural framework as shown in first column of FIGS. 9 and 10 (1100,1200). The corresponding outputs of the generative model trained withthe paired samples from the structural framework and its seismic image(FIGS. 9(b) and 11(a) respectively of Regone et al. 2017) are shown inthe second column of FIGS. 9 and 10 (1150, 1250). As shown in FIGS. 9and 10 , the generative model successfully mimics what it learned fromthe training data and outputs a realistic models in the sense of thetraining set.

In all practical applications, the present technological advancementmust be used in conjunction with a computer, programmed in accordancewith the disclosures herein. For example, FIG. 11 is a diagram of anexemplary computer system 1300 that may be utilized to implement methodsdescribed herein. A central processing unit (CPU) 1302 is coupled tosystem bus 1304. The CPU 1302 may be any general-purpose CPU, althoughother types of architectures of CPU 1302 (or other components ofexemplary computer system 1300) may be used as long as CPU 1302 (andother components of computer system 1300) supports the operations asdescribed herein. Those of ordinary skill in the art will appreciatethat, while only a single CPU 1302 is shown in FIG. 11 , additional CPUsmay be present. Moreover, the computer system 1300 may comprise anetworked, multi-processor computer system that may include a hybridparallel CPU/GPU system. The CPU 1302 may execute the various logicalinstructions according to various teachings disclosed herein. Forexample, the CPU 1302 may execute machine-level instructions forperforming processing according to the operational flow described.

The computer system 1300 may also include computer components such asnon-transitory, computer-readable media. Examples of computer-readablemedia include a random access memory (RAM) 1306, which may be SRAM,DRAM, SDRAM, or the like. The computer system 1300 may also includeadditional non-transitory, computer-readable media such as a read-onlymemory (ROM) 1308, which may be PROM, EPROM, EEPROM, or the like. RAM1306 and ROM 1308 hold user and system data and programs, as is known inthe art. The computer system 1300 may also include an input/output (I/O)adapter 1310, a graphics processing unit (GPU) 1314, a communicationsadapter 1322, a user interface adapter 1324, a display driver 1316, anda display adapter 1318.

The I/O adapter 1310 may connect additional non-transitory,computer-readable media such as storage device(s) 1312, including, forexample, a hard drive, a compact disc (CD) drive, a floppy disk drive, atape drive, and the like to computer system 1300. The storage device(s)may be used when RAM 1306 is insufficient for the memory requirementsassociated with storing data for operations of the present techniques.The data storage of the computer system 1300 may be used for storinginformation and/or other data used or generated as disclosed herein. Forexample, storage device(s) 1312 may be used to store configurationinformation or additional plug-ins in accordance with the presenttechniques. Further, user interface adapter 1324 couples user inputdevices, such as a keyboard 1328, a pointing device 1326 and/or outputdevices to the computer system 1300. The display adapter 1318 is drivenby the CPU 1302 to control the display on a display device 1320 to, forexample, present information to the user such as subsurface imagesgenerated according to methods described herein.

The architecture of computer system 1300 may be varied as desired. Forexample, any suitable processor-based device may be used, includingwithout limitation personal computers, laptop computers, computerworkstations, and multi-processor servers. Moreover, the presenttechnological advancement may be implemented on application specificintegrated circuits (ASICs) or very large scale integrated (VLSI)circuits. In fact, persons of ordinary skill in the art may use anynumber of suitable hardware structures capable of executing logicaloperations according to the present technological advancement. The term“processing circuit” encompasses a hardware processor (such as thosefound in the hardware devices noted above), ASICs, and VLSI circuits.Input data to the computer system 1300 may include various plug-ins andlibrary files. Input data may additionally include configurationinformation.

Preferably, the computer is a high performance computer (HPC), known tothose skilled in the art. Such high performance computers typicallyinvolve clusters of nodes, each node having multiple CPU's and computermemory that allow parallel computation. The models may be visualized andedited using any interactive visualization programs and associatedhardware, such as monitors and projectors. The architecture of systemmay vary and may be composed of any number of suitable hardwarestructures capable of executing logical operations and displaying theoutput according to the present technological advancement. Those ofordinary skill in the art are aware of suitable supercomputers availablefrom Cray or IBM or other cloud computing based vendors such asMicrosoft and Amazon.

The above-described techniques, and/or systems implementing suchtechniques, can further include hydrocarbon management based at least inpart upon the above techniques, including using the one or moregenerated geological models in one or more aspects of hydrocarbonmanagement. For instance, methods according to various embodiments mayinclude managing hydrocarbons based at least in part upon the one ormore generated geological models and data representations (e.g., seismicimages, feature probability maps, feature objects, etc.) constructedaccording to the above-described methods. In particular, such methodsmay include drilling a well, and/or causing a well to be drilled, basedat least in part upon the one or more generated geological models anddata representations discussed herein (e.g., such that the well islocated based at least in part upon a location determined from themodels and/or data representations, which location may optionally beinformed by other inputs, data, and/or analyses, as well) and furtherprospecting for and/or producing hydrocarbons using the well. Forexample, the different stages of exploration may result in data beinggenerated in the respective stages, which may be iteratively used by themachine learning to generate the one or more geological models discussedherein.

It is intended that the foregoing detailed description be understood asan illustration of selected forms that the invention can take and not asa definition of the invention. It is only the following claims,including all equivalents, that are intended to define the scope of theclaimed invention. Further, it should be noted that any aspect of any ofthe preferred embodiments described herein may be used alone or incombination with one another. Finally, persons skilled in the art willreadily recognize that in preferred implementation, some or all of thesteps in the disclosed method are performed using a computer so that themethodology is computer implemented. In such cases, the resultingphysical properties model may be downloaded or saved to computerstorage.

REFERENCES

The following references are hereby incorporated by reference herein intheir entirety:

-   T. Zhang, Incorporating Geological Conceptual Models and    Interpretations into Reservoir Modeling Using Multiple-Point    Geostatistics, Earth Science Frontiers, 15(1), 2008.-   J. Andersson and J. A. Hudson, T-H-M-C Modelling of Rock Mass    Behaviour—1: The Purposes, The Procedures and The Products,    Geo-Engineering, Elsevier, 2004, Pages 433-438-   I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D.    Warde-Farley, S. Ozair, A. Courville and Y. Bengio, Generative    Adversarial Networks, NIPS, 2014.-   P. Isola, J.-Y. Zhu, T. Zhou and A. A. Efros, Image-to-Image    Translation with Conditional Adversarial Networks,    arXiv:1611.07004v3, 2018.-   C. Regone, J. Stefani, P. Wang, C. Gerea, G. Gonzalez, and M.    Oristaglio, Geologic model building in SEAM Phase II—Land seismic    challenges, The Leading Edge, 2017.-   J. Y. Zhu, R. Zhang, D. Pathak, T. Darrell, A. A. Efros, O. Wang, E.    Shechtman, Toward Multimodal Image-to-Image Translation, NIPS, 2017.-   X. Chen, Y. Duan, R. Houthooft, J. Schulman and I. Sutskever,    InfoGAN: Interpretable Representation Learning by Information    Maximizing Generative Adversarial Nets, 2016; arXiv:1606.03657.-   W. Fedus, M. Rosca, B. Lakshminarayanan, A. M. Dai, S. Mohamed    and I. Goodfellow, Many Paths to Equilibrium: GANs Do Not Need to    Decrease A Divergence at Every Step, International Conference on    Learning Representations, 2018; arXiv:1710.08446

The invention claimed is:
 1. A machine learning method for generatingone or more geological models of a subsurface, the method comprising:accessing conditioning data for one stage of hydrocarbon managementrelated to the subsurface, the one stage comprising one of anexploration stage or a development stage; accessing one or moregeological concepts related to a target subsurface; accessing one ormore input geological models of the subsurface; training a firstiteration of a machine learning model using the conditioning data forthe one stage of hydrocarbon management, the one or more geologicalconcepts, and the one or more input geological models; generating, basedon the first iteration of the machine learning model, one or moregeological models; using the one or more geological models generatedbased on the first iteration of the machine learning model for the onestage of hydrocarbon management; accessing conditioning data for asubsequent stage of hydrocarbon management related to the subsurface,the subsequent stage comprising a different and later stage to the onestage and comprising one of the development stage or a production stage,the conditioning data for the subsequent stage being different from theconditioning data for the one stage; training a second iteration of themachine learning model using the conditioning data for the subsequentstage of hydrocarbon management, wherein the training of the seconditeration of the machine learning model is further dependent on one orboth of the conditioning data for the one stage of hydrocarbonmanagement used in the first iteration or the machine learning modeltrained in the first iteration; generating, based on the seconditeration of the machine learning model, one or more geological modelsfor the subsequent stage of hydrocarbon management; and using the one ormore geological models generated based on the second iteration of themachine learning model for the subsequent stage of hydrocarbonmanagement.
 2. The method of claim 1, wherein the one or more inputgeological models of the subsurface comprise one or more input reservoirmodels of the subsurface; and wherein the conditioning data for at leastone of the one stage of hydrocarbon management or the subsequent stageof hydrocarbon management comprises geophysical data including fieldseismic data or simulated seismic data.
 3. The method of claim 1,wherein the conditioning data for at least one of the one stage ofhydrocarbon management or the subsequent stage of hydrocarbon managementcomprises one or more of a structural framework, an internal reservoirarchitecture, or petrophysical property maps.
 4. The method of claim 1,wherein the machine learning model trained in at least one of the firstiteration or second iteration maps a fixed set of conditioning data forat least one of the one stage of hydrocarbon management or thesubsequent stage of hydrocarbon management and at least one of varyingnoise or varying latent code to a plurality of reservoir models.
 5. Themethod of claim 4, wherein the machine learning model trained in atleast one of the first iteration or second iteration comprises agenerative adversarial network (GAN) including a generator and adiscriminator.
 6. The method of claim 5, wherein the discriminatorcomprises a discriminator network model; and wherein the discriminatornetwork model comprises a classifier network model.
 7. The method ofclaim 5, wherein the generator comprises a generator network model; andwherein the generator network model comprises a U-net model.
 8. Themethod of claim 5, wherein the generator comprises a generator networkmodel; and wherein the generator network model comprises an autoencoderor variational autoencoder model including an encoder and a decoder. 9.The method of claim 5, wherein the one or more geological concepts areinput to the GAN.
 10. The method of claim 9, wherein the one or moreinput geological models of the subsurface comprise simulated reservoirmodels of the subsurface.
 11. The method of claim 9, further comprisingaccessing one or more reservoir stratigraphic configurations of areservoir model; wherein training the machine learning model in at leastone of the first iteration or second iteration is further performedbased on the one or more reservoir stratigraphic configurations of thereservoir model; and wherein the machine learning model trained in atleast one of the first iteration or second iteration learns to generatethe one or more reservoir stratigraphic configurations of the reservoirmodel by varying values of noise or latent code variables.
 12. Themethod of claim 5, wherein the GAN uses stratigraphic sketches andcorresponding seismic data or petrophysical data associated with seismicdata as a training set.
 13. The method of claim 5, wherein the GAN usescomputational stratigraphy to generate stratigraphic models and seismicsimulations or petrophysical data associated with seismic data as atraining set.
 14. The method of claim 1, wherein the conditioning datacomprises geophysical data; wherein the machine learning model trainedin at least one of the first iteration or second iteration generates aplurality of reservoir models based on the conditioning data for atleast one of the one stage of hydrocarbon management or the subsequentstage of hydrocarbon management and the one or more geological concepts;and further comprising quantifying uncertainty of anticipated reservoirperformance in the subsurface using the plurality of reservoir models.15. The method of claim 14, wherein quantifying uncertainty ofanticipated reservoir performance comprises estimating one or morestatistical distributions of target reservoir quantities including oneor more of: net-to-gross; spatial continuity; distribution of dynamicproperties affecting fluid flow conditions; or distribution ofpetrophysical properties.
 16. The method of claim 1, wherein using theone or more geological models based on the first iteration of themachine learning model or the second iteration of the machine learningmodel comprises modifying at least one of reservoir development,depletion, or management in the subsurface.
 17. The method of claim 16,wherein modifying at least one of reservoir development, depletion, ormanagement comprises modifying a trajectory of a borehole in the subsurface.
 18. The method of claim 1, wherein using the one or moregeological models based on the first iteration of the machine learningmodel or the second iteration of the machine learning model comprisescausing a well to be drilled in the subsurface based upon the one ormore geological models.
 19. The method of claim 1, wherein the one ormore geological models based on the first iteration of the machinelearning model or the second iteration of the machine learning model aregenerated for multiple stages of a life cycle of an oil and gas fieldincluding exploration, development and production.
 20. The method ofclaim 19, wherein the machine learning model trained in both the firstiteration and the second iteration comprises a generative adversarialnetwork (GAN) including a generator and a discriminator; and wherein thegenerator is iteratively updated or continually trained for multiplestages of the life cycle of an oil and gas field including theexploration stage, the development stage, and the production stage. 21.The method of claim 19, wherein in the first iteration, a first set ofgeological data is used by machine learning in order to generate a firstset of geological models; wherein in the second iteration, a second setof geological data is used by the machine learning in order to generatea second set of geological models; wherein the second set of geologicaldata is different from the first set of geological data; and wherein thefirst set of geological models is different from the second set ofgeological models.
 22. The method of claim 1, wherein the conditioningdata for at least one of the one stage of hydrocarbon management or thesubsequent stage of hydrocarbon management comprisessynthetically-generated conditioning data; and further comprising:manipulating or augmenting the synthetically-generated conditioning datawith structured noise; and using the manipulated or augmentedsynthetically-generated conditioning data in training the machinelearning model.
 23. The method of claim 22, wherein manipulating oraugmenting the synthetically-generated conditioning data comprises usinga style transfer approach in order to translate thesynthetically-generated conditioning data into field data bymanipulating a synthetic data style of the synthetically-generatedconditioning data or by adding noise to the synthetically-generatedconditioning data, the noise having a similar distribution as the fielddata.
 24. The method of claim 23, wherein the synthetically-generatedconditioning data is generated using one or more simulators; and furthercomprising selecting the style transfer approach from a plurality ofavailable style transfer approaches, wherein the selection of the styletransfer approach is specific to a geological basin, a data acquisitiontype, or processing workflows in order to account for effects notmodeled with the one or more simulators.
 25. The method of claim 1,wherein the machine learning model trained in the second iteration isbased on the machine learning model trained in the first iteration. 26.The method of claim 25, wherein training the second iteration of themachine learning model comprises fixing the machine learning model fromthe first iteration and expanding the machine learning model from thefirst iteration with an expanded part comprising additional layerstrained with the conditioning data from the subsequent stage ofhydrocarbon management.
 27. The method of claim 1, wherein training thesecond iteration of the machine learning model comprises retraining themachine learning model as a whole.
 28. The method of claim 27, whereinretraining the machine learning model as a whole uses the conditioningdata for the one stage of hydrocarbon management and the conditioningdata for the subsequent stage of hydrocarbon management.